hypergeo (version 1.2-14)

gosper: Evaluation of the hypergeometric function using Gosper's method

Description

Evaluation of the hypergeometric function using Gosper's method

Usage

hypergeo_gosper(A, B, C, z, tol = 0, maxiter = 2000)

Arguments

A,B,C

Parameters (real or complex)

z

Complex argument

tol

tolerance (passed to GCF())

maxiter

maximum number of iterations

Author

R code by Robin K. S. Hankin, transcribed from maxima code posted by Richard Fateman, who credited Bill Gosper

Details

Gosper provides a three-term recurrence which converges when \(z\) is close to a critical point.

Bill Gosper asserts that the recursion holds for values of \(z\) which are inside the cardioid (sqrt(8)*cos(t)-2*cos(2t), sqrt(8)*sin(t)-2*sin(2t)) (see examples section).

It is suggested that the recursion should only be used when the auxiliary parameters A, B,C are all \(\le 12\) in absolute value.

References

Original email was archived at https://www.ma.utexas.edu/pipermail/maxima/2006/000126.html but does not appear there now; and the wayback machine doesn't find it either.

See Also

hypergeo_contfrac

Examples

hypergeo_gosper(1.1,5.1,3.1,crit())

# Compare MMA: -0.192225 + 0.692328 I

t <- seq(from=0,to=2i*pi,len=100)
plot(exp(t)*(sqrt(8)-exp(t)),asp=1,type='l')
points(crit())